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Convexity of chance constrained programming problems with respect to a new generalized concavity notion

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  • Zahra Mashayekhi Zadeh
  • Esmaile Khorram

Abstract

In this paper, convexity of chance constrained problems have been investigated. A new generalization of convexity concept, named h-concavity, has been introduced and it has been shown that this new concept is the generalization of the α-concavity. Then, using the new concept, some of the previous results obtained by Shapiro et al. [in Lecture Notes on Stochastic Programming Modeling and Theory, SIAM and MPS, 2009 ] on properties of α-concave functions, have been extended. Next the convexity of chance constraints with independent random variables is investigated. It will be shown how concavity properties of the mapping related to the decision vector have to be combined with suitable properties of decrease or increase for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels and then sufficient conditions for convexity of chance constrained problems which has been introduced by Henrion and Strugarek [in Convexity of chance constraints with independent random variables. Comput. Optim. Appl. 41:263–276, 2008 ] has been extended in this paper for a wider class of real functions. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Zahra Mashayekhi Zadeh & Esmaile Khorram, 2012. "Convexity of chance constrained programming problems with respect to a new generalized concavity notion," Annals of Operations Research, Springer, vol. 196(1), pages 651-662, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:651-662:10.1007/s10479-012-1105-6
    DOI: 10.1007/s10479-012-1105-6
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    References listed on IDEAS

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    1. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    2. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
    3. Vijay S. Bawa, 1973. "On Chance Constrained Programming Problems with Joint Constraints," Management Science, INFORMS, vol. 19(11), pages 1326-1331, July.
    4. Asgeir Tomasgard & Jan Audestad & Shane Dye & Leen Stougie & Maarten van der Vlerk & Stein Wallace, 1998. "Modelling aspects of distributed processingin telecommunication networks," Annals of Operations Research, Springer, vol. 82(0), pages 161-185, August.
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    Cited by:

    1. Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.

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